Optimization method for screen surface dynamic load of vibrating screen

ABSTRACT

The present invention discloses an optimization method for a screen surface dynamic load of a vibrating screen. The method includes the following steps: step 1. selecting design variables, and establishing an experimental matrix; step 2. performing a response curved surface experiment; step 3. establishing two double-objective optimization models and solving the same to obtain two groups of Pareto solution sets, wherein the solution sets respectively represent screening efficiency optimization paths of the vibrating screen under the conditions of a high screen surface dynamic load and a low screen surface dynamic load; and step 4. calculating an optimization space for a screen surface dynamic load under a high screening efficiency. According to the method of the present invention, the screen surface dynamic load can be directly reduced, and the service life of the screen surface and the whole vibrating screen is prolonged.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application claims priority to Chinese patent application No.2021106569961, filed on Jun. 11, 2021, the entire contents of which areincorporated herein by reference.

TECHNICAL FIELD

The present invention belongs to the technical field of mechanicalequipment, and relates to a vibrating screen, in particular to anoptimization method for a screen surface dynamic load of a vibratingscreen.

BACKGROUND

A vibrating screen works by using a reciprocating rotary vibrationgenerated by vibrator excitation. An upper rotating heavy hammer of avibrator causes a screen surface to generate a plane whirling vibration,while a lower rotating heavy hammer causes the screen surface togenerate a conical surface whirling vibration. Such a combined effectmakes the screen surface generate a compound whirling vibration. Anamplitude can be changed by adjusting the exciting forces of the upperand lower rotating heavy hammers. By adjusting spatial phase angles ofthe upper and lower heavy hammer, a curve shape of a movement trajectoryof the screen surface and a movement trajectory of materials on thescreen surface can be changed.

The vibrating screen separates granular materials according to thegranularity through a high-frequency vibration, and thus is widely usedin coal mines, agriculture, metallurgy and other fields owing to itssimple structure and efficient production. There is a huge demand forvibrating screens with high screening performances, stable structuralperformances and long service life in the industry.

The prior art has the following major problems and defects.

The research on the screening process of the vibrating screen focuses ona screening efficiency, i.e., performs screening efficiency optimizationfrom process parameters, motion forms, screen surface structures and thelike by using methods such as physical experiments, theoreticalderivation, and virtual simulation. However, a screen surface dynamicload is not considered in the optimization process, which improves thescreening efficiency, but the screen surface dynamic load is notreduced, and even possibly increased. An excessive screen surfacedynamic load will directly accelerate the corrosion of the screensurface structure, and indirectly increase loads on a side plate, anauxiliary beam and other structures of the vibrating screen, resultingin an adverse effect that the service life of the whole vibrating screenis short and the service life of the screen surface is relativelyshorter. By adding the auxiliary beam to improve the structuralperformance of the screen surface, although the stress and strainconcentration on the screen surface can be alleviated, the impactcorrosion on the screen surface and the forces on a screen box and avibration isolation system cannot be reduced, and an effective screeningarea of the screen surface may also be reduced, thereby affecting thescreening efficiency.

SUMMARY

With respect to the above problems and defects existing in the priorart, the present invention provides an optimization method for a screensurface dynamic load of a vibrating screen, which can reduce the screensurface dynamic load directly, reduce an overall structural load of ascreening machine indirectly, and prolong the service life of the screensurface and the whole vibrating screen.

Therefore, the present invention adopts the following technicalsolutions.

An optimization method for a screen surface dynamic load of a vibratingscreen includes the following steps:

step 1. selecting design variables, and establishing an experimentalmatrix;

step 2. performing a response curved surface experiment;

step 3. establishing two double-objective optimization models andsolving the same to obtain two groups of Pareto solution sets, whereinthe solution sets respectively represent screening efficiencyoptimization paths of the vibrating screen under the conditions of ahigh screen surface dynamic load and a low screen surface dynamic load;and

step 4. calculating an optimization space for the screen surface dynamicload under a high screening efficiency.

Preferably, in the step 1. the method of establishing the experimentalmatrix includes:

S11. selecting factors that have a greater impact on the screeningefficiency and the screen surface dynamic load as design variables;

S12. determining factor levels, and determining the experimental matrixby using a center-circumscribed compound method; and

S13. performing a pre-experimental test on the experimental matrix.

Preferably, in Sit, the number of the design variables is preferably3-4; and the design variables include an excitation parameter, a screenmesh shape, and a screen surface inclination angle.

Preferably, in S13, the process of performing the pre-experimental teston the experimental matrix includes the following steps:

S131. calculating a throwing index τ or a vibration intensity K_(v) ofthe screen surface in all the experimental points in an experimentaltable:

${\tau = \frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha}},$${K_{v} = \frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha}};$

wherein A represents a vibration amplitude; f represents a vibrationfrequency; g represents an acceleration of gravity; β represents avibration direction angle; α represents a screen surface inclinationangle; w represents an angular frequency;

S132. selecting three experimental points with the lowest throwing indexor vibration intensity of the screen surface in the experimental matrixfor pre-experiment; and

S133. determining whether material screening systems corresponding tothe three pre-experiment points can reach a steady state, and completingthe pre-experiment if all material screening systems reach a steadystate, otherwise returning to the step S12 to re-adjust the factorlevels.

Preferably, in S133, the method of determining whether the materialscreening systems corresponding to the three pre-experiment points canreach the steady state includes: acquiring an acceleration signal on aside plate of the vibrating screen through an accelerometer, andconsidering that the material screening system reaches the steady stateif the signal reaches a steady state.

Preferably, in the step 3, the process of establishing the twodouble-objective optimization models and solving the same includes:

S31: establishing a mathematical model of the screening efficiency andthe screen surface dynamic load through multiple linear regression;

S32: establishing two double-objective optimization models; and

S33: solving the two double-objective optimization problems by applyingan NSGA-II algorithm to obtain two groups of Pareto solution sets.

Preferably, in S31, evaluation indexes for the screening efficiency areshown in the following formulas:

M _(c)=100γ_(c) Q _(f),

M _(f)=100γ_(f) Q _(c),

F _(c)=γ_(c) −M _(c) +M _(f),

F _(f)=γ_(f) −M _(f) +M _(c),

${E_{c} = \frac{\gamma_{c} - M_{f}}{F_{c}}},$${E_{f} = \frac{\gamma_{f} - M_{f}}{F_{f}}},$η=E _(c) +E _(f)−100;

wherein M_(e) is the content of misplaced materials in screen overflow,that is, a percentage of fine particles in the screen overflow to thefeed, %; M_(f) is the content of misplaced materials in screenunderflow, that is, a percentage of coarse particles in the screenunderflow to the feed, %; γ_(c) is an actual yield of the screenoverflow, %; γ_(f) is an actual yield of the screen underflow, %; Q_(f)is the content of fine particles in the screen overflow,%; Q_(c) is thecontent of the coarse particles in the screen underflow, %; F_(c) is thecontent of coarse particles in the feed, that is, a theoretical yield ofthe screen overflow, %; F_(f) is the content of fine particles in thefeed, that is, a theoretical yield of the screen underflow, %; E_(c) isa positive matching efficiency of coarse particles, %; E_(f) is apositive matching efficiency of fine particles, %; η is the screeningefficiency, %;

a screen surface dynamic load index takes a mean value of differencesbetween peak values of a stress signal at the connection between ascreen surface structure and a side plate under unloaded and loadedconditions of the vibrating screen as a quantitative index, denoted asF, and is calculated according to the following formula:

${F = {\sum\limits_{i = 1}^{n}\overset{\_}{\Delta F_{i}}}},$${\overset{\_}{\Delta F_{i}} = {\overset{\_}{F_{i{load}}} - \overset{\_}{F_{i{unload}}}}};$

wherein

$\overset{\_}{F_{i{load}}}{and}\overset{\_}{F_{i{unload}}}$

are mean values of maximum stress values at an i^(th) measuring point inunit time under the stable loaded and unloaded states of a screeningmachine, respectively.

Preferably, in S32, the double-objective optimization models are asfollows:

$\left\{ {\begin{matrix}{{Max}\left( M_{Efficiency} \right)} \\{{Max}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix},} \right.$ $\left\{ {\begin{matrix}{{Min}\left( M_{Efficiency} \right)} \\{{Min}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix};} \right.$

wherein M_(efficiency) represents a function expression of the screeningefficiency; M_(load) represents a function expression of the screensurface dynamic load; a₁ represents a minimum value of a throwing indexof the screen surface in an experimental point; a₂ represents a minimumvalue of a vibration intensity in the experimental point; A representsthe vibration amplitude; g represents the acceleration of gravity; βrepresents the vibration direction angle; α represents the screensurface inclination angle; X_(i) represents a variable in an objectivefunction; X_(imin) represents a lower limit of the variable X_(i); andX_(imin) represents an upper limit of the variable X.

Preferably, in S33, a solution set obtained according to

$\left\{ \begin{matrix}{{Max}\left( M_{Efficiency} \right)} \\{{Max}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right.$

is taken as a first solution set, and a solution set obtained accordingto

$\left\{ \begin{matrix}{{Min}\left( M_{Efficiency} \right)} \\{{Min}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right.$

is taken as a second solution set.

Preferably, in step 4, the calculation formula is as follows:

$\left( {{Optimization}{space}} \right)_{i} = \frac{\left( {{screen}{surface}{dynamic}{load}} \right)_{i1} - \left( {{screen}{surface}{dynamic}{load}} \right)_{i2}}{\left( {{screen}{surface}{dynamic}{load}} \right)_{i2}}$

wherein the (optimization space), represents an optimization space for ascreen surface dynamic load under a certain screening efficiency level;the (screen surface dynamic load)_(i1) represents a screen surfacedynamic load value in the first solution set corresponding to thisscreening efficiency; and the (screen surface dynamic load)_(i2)represents a screen surface load value in the second solution setcorresponding to this screening efficiency.

Compared with the prior art, the method of the present invention has thefollowing technical effects:

(1) a process parameter configuration scheme of the vibrating screenthat can simultaneously achieve a high screening efficiency and a lowscreen surface dynamic load can be obtained;

(2) the screen surface dynamic load can be directly reduced, the overallstructural load of the screening machine is indirectly reduced, and theservice life of the screen surface and the whole vibrating screen isprolonged; and

(3) an effective screening area of the screen surface is improved, andan optimization space is increased.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a flowchart of an optimization method for a screen surfacedynamic load of a vibrating screen as provided by an embodiment of thepresent invention.

FIG. 2 is a schematic diagram of positional layout of stress sensors fora side plate on a screen surface in the embodiment of the presentinvention.

FIG. 3 is a schematic diagram of positional layout of accelerationsensors for the side plate on the screen surface in the embodiment ofthe present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention discloses an optimization method for a screensurface dynamic load of a vibrating screen, which solves the problems inthe prior art that a vibrating screen is seriously affected by particleimpact, resulting in low structural performances of a screening machineand short service life of the screening machine.

The above objective of the present invention is achieved by thefollowing technical solutions.

An optimization method for a screen surface dynamic load of a vibratingscreen includes the following steps:

S1. selecting design variables, and establishing an experimental matrix;

S2. performing a response curved surface experiment;

S3. establishing two double-objective optimization models and solvingthe same to obtain two groups of Pareto solution sets, wherein thesolution sets respectively represent screening efficiency optimizationpaths of the vibrating screen under the conditions of a high screensurface dynamic load and a low screen surface dynamic load; and

S4, calculating an optimization space for the screen surface dynamicload under a high screening efficiency, wherein a specific calculationmethod is shown in Formula 1:

$\begin{matrix}{\left( {{Optimization}{space}} \right)_{i} = \frac{\left( {{screen}{surface}{load}} \right)_{i1} - \left( {{screen}{surface}{load}} \right)_{i2}}{\left( {{screen}{surface}{load}} \right)_{i2}}} & (1)\end{matrix}$

wherein an (optimization space)_(i) represents an optimization space fora screen surface dynamic load under a certain screening efficiencylevel; a (screen surface dynamic load)_(i1) represents a screen surfacedynamic load value in the first solution set corresponding to thisscreening efficiency; and the (screen surface dynamic load)_(i2)represents a screen surface dynamic load value in the second solutionset corresponding to this screening efficiency.

In the step S1, the method of selecting the design variables andestablishing the experimental matrix includes:

S11. selecting factors that have a greater impact on the screeningefficiency and the screen surface dynamic load as design variables, suchas an excitation parameter, a screen mesh shape, and a screen surfaceinclination angle, wherein the number of the design variables ispreferably 3-4;

S12. determining factor levels, and determining the experimental matrixby using a center-circumscribed compound (CCC) method; and

S13. performing a pre-experimental test on the experimental matrix.

In S13. the method of performing the pre-experimental test on theexperimental matrix includes the following specific steps:

S131. calculating a throwing index τ or a vibration intensity K_(v) ofthe screen surface in all the experimental points in an experimentaltable;

$\begin{matrix}{\tau = \frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha}} & (2)\end{matrix}$ $\begin{matrix}{K_{v} = \frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha}} & (3)\end{matrix}$

S132. selecting three experimental points with the lowest throwing indexor lowest vibration intensity of the screen surface in the experimentalmatrix for pre-experiment; and

S133. determining whether material screening systems corresponding tothe three pre-experiment points can reach a steady state, and completingthe pre-experiment if all material screening systems reach a steadystate, otherwise returning to the step S12 to re-adjust the factorlevels.

In S133, the method of determining whether the material screeningsystems corresponding to the three pre-experiment points can reach thesteady state includes: acquiring an acceleration signal on a side plateof the vibrating screen through an accelerometer, and considering thatthe material screening system reaches the steady state if the signalreaches a steady state.

In the step 2, the process of establishing the two double-objectiveoptimization models and solving the same includes:

S21: establishing mathematical models of the screening efficiency andthe screen surface dynamic load through multiple linear regression,wherein evaluation indexes of the screening efficiency are shown inFormulas 4-10:

M _(c)=100γ_(c) Q _(f)  (4)

M _(f)=100γ_(f) Q _(c)  (5)

F _(c)=γ_(c) −M _(c) +M _(f)  (6)

F _(f)=γ_(f) −M _(f) +M _(c)  (7)

$\begin{matrix}{E_{c} = \frac{\gamma_{c} - M_{f}}{F_{c}}} & (8)\end{matrix}$ $\begin{matrix}{E_{f} = \frac{\gamma_{f} - M_{f}}{F_{f}}} & (9)\end{matrix}$η=E _(c) +E _(f)−100  (10)

wherein M_(c) is the content of misplaced materials in screen overflow(coarse particles), that is, a percentage of fine particles in thescreen overflow to the feed, %; M_(f) is the content of misplacedmaterials in screen underflow (fine particles), that is, a percentage ofcoarse particles in the screen underflow to the feed, %; γ_(c) is anactual yield of the screen overflow (coarse particles), %; γ_(f) is anactual yield of the screen underflow (fine particles), %; Q_(f) is thecontent of fine particles in the screen overflow (coarse particles),%;Q_(c) is the content of the coarse particles in the screen underflow(fine particles), %; F_(c) is the content of coarse particles in thefeed, that is, a theoretical yield of the screen overflow (coarseparticles), %; F_(f) is the content of fine particles in the feed, thatis, a theoretical yield of the screen underflow (fine particles), %;E_(c) is a positive matching efficiency of coarse particles, %; E_(f) isa positive matching efficiency of fine particles. %; and η is thescreening efficiency, %;

a screen surface dynamic load index takes a mean value of differencesbetween peak values of a stress signal at the connection between ascreen surface structure and the side plate under unloaded and loadedconditions of the vibrating screen as a quantitative index, denoted asF; the specific calculation formulas are shown in Formula 11 and Formula12, wherein

$\overset{\_}{F_{i{load}}}$

and

$\overset{\_}{F_{i{unload}}}$

are mean values of maximum stress values at an i^(th) measuring point inunit time under the stable loaded and unloaded states of the screenmachine, respectively;

$\begin{matrix}{F = {\sum\limits_{i = 1}^{n}\overset{\_}{\Delta F_{i}}}} & (11)\end{matrix}$ $\begin{matrix}{\overset{\_}{\Delta F_{i}} = {\overset{\_}{F_{i{load}}} - \overset{\_}{F_{i{unload}}}}} & (12)\end{matrix}$

S22: establishing two double-objective optimization models, which arespecifically as shown in the following formulas:

$\begin{matrix}\left\{ \begin{matrix}{{Max}\left( M_{Efficiency} \right)} \\{{Max}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right. & (13)\end{matrix}$ $\begin{matrix}\left\{ \begin{matrix}{{Min}\left( M_{Efficiency} \right)} \\{{Min}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right. & (14)\end{matrix}$

wherein M_(efficiency) represents a function expression of the screeningefficiency; M_(load) represents a function expression of the screensurface dynamic load; a₁ represents a minimum value of a throwing indexof the screen surface in an experimental point; a₂ represents a minimumvalue of a vibration intensity in the experimental point; A representsthe vibration amplitude; g represents the acceleration of gravity; βrepresents the vibration direction angle; α represents the screensurface inclination angle; X_(i) represents a variable in an objectivefunction; X_(imin) represents a lower limit of the variable X_(i); andX_(iman) represents an upper limit of the variable X_(i); and

S23: solving two double-objective optimization problems by applying anNSGA-II algorithm to obtain two groups of Pareto solution sets. Asolution set obtained according to Formula 13 is taken as a firstsolution set, and a solution set obtained according to Formula (14) istaken as a second solution set.

Embodiments

As shown in FIG. 1 , the present invention provides an optimizationmethod for a screen surface dynamic load of a vibrating screen. In thisembodiment, experiments are carried out with linear screens. The size ofa screen surface of each linear screen is 2,000 mm*1,300 mm, and ascreen surface inclination angle can be adjusted by a support structure.There are four stress sensors in total, namely a first stress sensor1-1, a second stress sensor 1-2, a third stress sensor 1-3, and a fourthstress sensor 1-4 respectively, and their arrangement positions areshown in FIG. 2 . There are two acceleration sensors in total, namely afirst acceleration sensor 2-1 and a second acceleration sensor 2-2respectively, and their arrangement positions are shown in FIG. 3 .

In S1: experiments are performed by using the linear screens. Excitationparameters (amplitude, frequency, and vibration direction angle) and thescreen surface inclination angle are selected as design variables, and afeed flow rate is set to 16 t/h. A set of effective experimentalmatrices are determined through pre-experiments, and the specific factorlevel settings and experimental tables are shown in Tables 1 and 2.Based on relevant theories of a stochastic process, in each group ofexperiments, whether a steady state is reached is determined through theacceleration sensors, particle size distribution and stress data ofparticles over and under the screen in the steady state are collected,and the screen surface dynamic load and the screening efficiency data inthe experiments obtained by calculation are shown in Table 2. Acalculation formula for the screen surface load is shown in Formula 15:

$\begin{matrix}{F = {{0.1\overset{\_}{\Delta F_{1}}} + {0.2\overset{\_}{\Delta F_{2}}} + {0.3\overset{\_}{\Delta F_{3}}} + {0.4{\overset{\_}{\Delta F_{4}}.}}}} & (15)\end{matrix}$

TABLE 1 Design variables and factor level settings Level Factor −2 −1 01 2 A(mm) 6.5 5.5 4.5 3.5 2.5 f(Hz) 12 14.5 17 19.5 22 α(°) 2 4.5 7 9.512 β(°) 40 45 50 55 60

TABLE 2 Design variables and factor level settings Screen surfaceVibration Screening Operating inclination direction efficiency Screensurface sequence Amplitude Frequency angle angle (%) load (N) S −1 −1 −1−1 85.026 3.2629 2 0 0 0 0 81.649 2.9097 3 0 0 0 −2 83.633 2.7794 4 1 −1−1 −1 89.172 3.7480 5 0 0 0 0 81.165 2.8000 6 0 −2 0 0 88.36 3.3472 7 −11 1 1 67.205 2.7970 8 −1 −1 −1 1 84.351 3.9317 9 0 0 0 0 81.29 2.8728 100 2 0 0 73.891 2.9012 11 2 0 0 0 86.144 3.1731 12 0 0 −2 0 85.913 4.250013 −1 −1 1 −1 79.859 2.5077 14 −1 1 −1 1 75.618 3.6539 15 0 0 0 0 81.782.9262 16 −2 0 0 0 74.398 2.9219 17 0 0 0 0 81.577 2.8464 18 1 −1 1 183.098 2.8907 19 0 0 0 0 81 2.9024 20 1 −1 −1 1 89.106 4.7786 21 0 0 0 280.595 3.5892 22 1 1 1 −1 79.029 2.4312 23 1 −1 1 −1 85.198 2.6472 24 −11 1 −1 71.963 2.4563 25 −1 1 −1 −1 76.983 3.0416 26 1 1 −1 1 82.8373.8878 27 0 0 0 0 81.492 2.8501 28 1 1 1 1 76.053 2.7751 29 −1 −1 1 177.542 2.8018 30 1 1 −1 −1 84.05 3.1497 31 0 0 2 0 73.865 2.4410

In S2: functional relationships among the screen surface load, thescreening efficiency and the design variables are establishedrespectively by using a multiple linear regression method. As shown inFIG. 16 and FIG. 17 , M_(e) is the screening efficiency, and M_(s) isthe screen surface load. Therefore, the two double-objectiveoptimization models are established and shown in Formulas 18 and 19.

M_(e)=0.885+0.0624x1−0.00108x2+0.00506x3+0.000351x4−0.00621x1x1−0.000034x2x2−0.000728x3x3−0.002039x1x20.000742xx3+0.000044x2x3−0.000036x2x4−0.000056x3x4  (16)

M _(s)=14.01−1.671x1−0.602x2−0.715x3+0.0651x4−0.0475x1x1+0.00734x2x2+0.01620x3x3+0.0422x1x2+0.0498x1x3+0.01600x2x30.00050x2x4−0.00457x3x4  (17)

$\begin{matrix}\left\{ {s.t.\begin{matrix}{\min{M_{s}\left( {x_{1},x_{2},x_{3},x_{4}} \right)}} & \text{ } \\{\min{M_{e}\left( {x_{1},x_{2},x_{3},x_{4}} \right)}} & \text{ } \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > 3.3} & \text{ } \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > 3.5} & \text{ } \\{x_{imin} < x_{i} < x_{imax}} & {{i \in 1},2,3,4}\end{matrix}} \right. & (18)\end{matrix}$ $\begin{matrix}\left\{ {s.t.\begin{matrix}{\max{M_{s}\left( {x_{1},x_{2},x_{3},x_{4}} \right)}} & \text{ } \\{\max{M_{e}\left( {x_{1},x_{2},x_{3},x_{4}} \right)}} & \text{ } \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > 3.3} & \text{ } \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > 3.5} & \text{ } \\{x_{imin} < x_{i} < x_{imax}} & {{i \in 1},2,3,4}\end{matrix}} \right. & (19)\end{matrix}$

In S3, two groups of Pareto solution sets are solved by using an NSGA-IIalgorithm, wherein the solution sets respectively represent screeningefficiency optimization paths of the vibrating screen under theconditions of a high screen surface dynamic load and a low screensurface dynamic load.

In S4: the screen surface dynamic load under a high screening efficiencyis calculated to optimize an optimization space. When the screeningefficiency is 80%, a space for the screen surface load can be optimizedby about 39%; when the screening efficiency is 85%, a space for thescreen surface load can be optimized by about 26%; the screeningefficiency is 90%, a space for the screen surface load can be optimizedby about 18%.

A configuration scheme of some process parameters in the optimizationpath of the low screen surface load is shown in Table 3.

TABLE 3 Configuration scheme of process parameters of the low screensurface load during the vibration under a high screening efficiencyInclination Direction Screen surface Screening Sequence AmplitudeFrequency angle angle dynamic load efficiency 1 3.72 16.98 2.03 69.986.210 7.089 2 365 20.38 2.09 69.98 5.752 6.097 3 4.01 21.66 2.08 69.975.469 5.580 4 4.86 21.87 2.1 69.98 5.282 5.356 5 5.57 21.91 2.09 69.995.161 5.191

1. An optimization method for a screen surface dynamic load of avibrating screen, comprising following steps: step
 1. selecting designvariables, and establishing an experimental matrix; step
 2. performing aresponse curved surface experiment; step
 3. establishing twodouble-objective optimization models and solving the twodouble-objective optimization models to obtain two groups of Paretosolution sets, wherein the two groups of Pareto solution setsrespectively represent screening efficiency optimization paths of thevibrating screen under conditions of a high screen surface dynamic loadand a low screen surface dynamic load; and step
 4. calculating anoptimization space for the screen surface dynamic load under a highscreening efficiency, wherein: in the step 3, the method of establishingthe two double-objective optimization models and solving the twodouble-objective optimization models comprises: establishingmathematical models of screening efficiency and the screen surfacedynamic load through multiple linear regression; establishing the twodouble-objective optimization models; and solving two double-objectiveoptimization problems by applying a non-dominated sorting geneticalgorithm-IL NSGA-II, to obtain the two groups of Pareto solution sets;in the method of establishing mathematical models of the screeningefficiency and the screen surface dynamic load, evaluation indexes forthe screening efficiency are shown in following formulas:M _(c)=100γ_(c) Q _(f),M _(f)=100γ_(f) Q _(c),P _(c)=γ_(c) −M _(c) +M _(f),F _(f)=γ_(f) −M _(f) +M _(c),${E_{c} = \frac{\gamma_{c} - M_{f}}{F_{c}}},$ ${E_{f} = \begin{matrix}\gamma_{f} & \text{ } & M_{f} \\\text{ } & F_{f} & \text{ }\end{matrix}},$η=E _(c) +E _(f)−100; wherein M_(c) is content of misplaced materials inscreen overflow, that is, a percentage of fine particles in the screenoverflow to a feed, %; M_(f) is the content of the misplaced materialsin screen underflow, that is, a percentage of coarse particles in thescreen underflow to the feed, %; γ_(c) is an actual yield of the screenoverflow, %; γ_(f) is an actual yield of the screen underflow, %; Q_(f)is content of the fine particles in the screen overflow, %; Q_(c) iscontent of the coarse particles in the screen underflow, %; F_(c) is thecontent of the coarse particles in the feed, that is, a theoreticalyield of the screen overflow, %; F_(f) is the content of the fineparticles in the feed, that is, a theoretical yield of the screenunderflow, %; E_(c) is a positive matching efficiency of the coarseparticles, %; E_(f) is a positive matching efficiency of the fineparticles, %; η is the screening efficiency, %; a screen surface dynamicload index takes a mean value of differences between peak values of astress signal at a connection between a screen surface structure and aside plate under unloaded and loaded conditions of the vibrating screenas a quantitative index, denoted as F, and is calculated according tothe following formulas:${F = {\sum\limits_{i = 1}^{n}\overset{\_}{\Delta F_{i}}}},$${\overset{\_}{\Delta F_{i}} = {\overset{\_}{F_{i{load}}} - \overset{\_}{F_{i{unload}}}}};$wherein $\overset{\_}{F_{i{load}}}$ and $\overset{\_}{F_{i{unload}}}$are mean values of maximum stress values at an i^(th) measuring point inunit time under stable loaded and unloaded states of a screeningmachine, respectively; in the method of establishing the twodouble-objective optimization models, the double-objective optimizationmodels are as follows: $\left\{ {\begin{matrix}{{Max}\left( M_{Efficiency} \right)} \\{{Max}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix},} \right.$ $\left\{ {\begin{matrix}{{Min}\left( M_{Efficiency} \right)} \\{{Min}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix};} \right.$ wherein M_(efficiency) represents a functionexpression of the screening efficiency; M_(load) represents a functionexpression of the screen surface dynamic load; a₁ represents a minimumvalue of a throwing index of the screen surface in an experimentalpoint; a₂ represents a minimum value of a vibration intensity in theexperimental point; A represents a vibration amplitude; g represents anacceleration of gravity; β represents a vibration direction angle; arepresents a screen surface inclination angle; w represents an angularfrequency; f represents a vibration frequency; X_(i) represents avariable in an objective function; X_(imin) represents a lower limit ofthe variable X_(i); and X_(imax) represents an upper limit of thevariable X_(i); in the method of solving the two double-objectiveoptimization problems by applying the NSGA-II, a solution set obtainedaccording to $\left\{ \begin{matrix}{{Max}\left( M_{Efficiency} \right)} \\{{Max}\left( M_{load} \right)} \\{\begin{matrix}{{Aw}^{2}\sin\beta} \\{{\mathcal{g}}\cos\alpha}\end{matrix} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right.$ is taken as a first solution set, and a solutionset obtained according to $\left\{ \begin{matrix}{{Min}\left( M_{Efficiency} \right)} \\{{Min}\left( M_{load} \right)} \\{\frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha} > a_{1}} \\{\frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha} > a_{2}} \\{x_{imin} < x_{i} < x_{imax}}\end{matrix} \right.$ is taken as a second solution set; and in the step4, a calculation formula is as follows:${\left( {{Optimization}{space}} \right)_{i} = \frac{\left( {{screen}{surface}{dynamic}{load}} \right)_{i1} - \left( {{screen}{surface}{dynamic}{load}} \right)_{i2}}{\left( {{screen}{surface}{dynamic}{load}} \right)_{i2}}};$wherein, the (optimization space)_(i) represents the optimization spacefor the screen surface dynamic load under a certain screening efficiencylevel; the (screen surface dynamic load)_(i1) represents a screensurface dynamic load value in the first solution set corresponding tothe screening efficiency; and the (screen surface dynamic load)_(i2)represents a screen surface dynamic load value in the second solutionset corresponding to the screening efficiency.
 2. The optimizationmethod for the screen surface dynamic load of the vibrating screenaccording to claim 1, wherein in the step 1, the method of establishingthe experimental matrix comprises: selecting factors that have a greaterimpact on the screening efficiency and the screen surface dynamic loadas the design variables; determining factor levels, and determining theexperimental matrix by using a center-circumscribed compound method; andperforming a pre-experimental test on the experimental matrix.
 3. Theoptimization method for the screen surface dynamic load of the vibratingscreen according to claim 2, wherein in the method of selecting factors,a number of the design variables is either 3 or 4; and the designvariables include an excitation parameter, a screen mesh shape, andJhe_screen surface inclination angle.
 4. The optimization method for thescreen surface dynamic load of the vibrating screen according to claim2, wherein, the method of performing the pre-experimental test on theexperimental matrix comprises the following steps: calculating thethrowing index τ or the vibration intensity K_(v) of the screen surfacein all experimental points in an experimental table;${\tau - \frac{{A\left( {2\pi f} \right)}^{2}}{{\mathcal{g}}\cos\alpha}},$${K_{v} - \frac{{Aw}^{2}\sin\beta}{{\mathcal{g}}\cos\alpha}};$ wherein Arepresents the vibration amplitude; f represents the vibrationfrequency; g represents the acceleration of gravity; β represents thevibration direction angle; α represents the screen surface inclinationangle; w represents the angular frequency; selecting three experimentalpoints with the lowest throwing index or lowest vibration intensity ofthe screen surface in the experimental matrix for pre-experiment; anddetermining whether material screening systems corresponding to threepre-experiment points can reach a steady state, and completing thepre-experiment test if all material screening systems reach the steadystate, otherwise returning to re-adjust the factor levels.
 5. Theoptimization method for the screen surface dynamic load of the vibratingscreen according to claim 4, wherein, the method of determining whetherthe material screening systems corresponding to the three pre-experimentpoints can reach the steady state, comprising the following steps:acquiring an acceleration signal on the side plate of the vibratingscreen through an accelerometer, and determining that the materialscreening system reaches the steady state if the acceleration signalreaches a steady state.